The singular value decomposition (SVD) of an m-by-n matrix A is given by
where U and V are orthogonal (unitary)
and 
is an m-by-n diagonal matrix with real
diagonal elements, 
, such that
The are the singular values of A and the
first min(m,n) columns of U and V
are the left and right singular vectors of A.
The singular values and singular vectors satisfy
where 
and 
are the ith columns of U and V, respectively.
A single driver routine, PxGESVD , computes the ``economy size'' or
``thin'' singular value decomposition of a general nonsymmetric matrix
(see table 3.4). Thus, if A is m-by-n with
m>n, then only the first n columns of U are computed and is an
n-by-n matrix. For a detailed discussion of the ``thin'' singular
value decomposition, refer to [71, p. 72,].
Currently, only PSGESVD and PDGESVD are provided.
Table 3.4: Driver routines for standard eigenvalue and singular value problems